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Unpacking “ESTEEM”
• Excel: ubiquitous, easy, flexible, non-intimidating
• Exploratory: apply to real-world data; extend & improve
• Experiential: students engage directly with the math
The ESTEEEM Project Homepage
• 55 modules:Broad range of topicsand data sets
• Go to Island Biogeography
http://bioquest.org/esteem
Module Main Page
• Screenshots &brief description
• Mathematical expression
• Research articles& primary data
• User manual & curriculum materials(in progress)
• DownloadableExcel sheet
Population genetics
Population growth Bioinformatics
Operon function
PhylogeneticsEpidemiology
Protein structureEnzyme kinetics
Three Boxes
Black box:Hide the model
? y = axb
Glass box:Study the model
y = axb
No box:Build the model!
How do students interact with the mathematical model underlying the biology?
Copyleft
• download• use• modify• share
Users may freely the software, w/proper attribution
More info available at Free Software Foundation website
Continuous Growth ModelsBiological Goals:
• Explore the growth of microbial populations
• Discriminate among alternate hypotheses
Quantitative Goals:
• Distinguish between absolute & relative, limited & unlimited growth
• Gain hands-on experience with selecting & fitting models
Continuous Growth Models1. Wet lab portion
• Inoculate bread
• Take digital pictures at 1-day intervals
• Calculate mold area using ImageJ (Mac) or Scion Image (PC) — or have students estimate area!
Prediction:What pattern of growth will you see?
Continuous Growth Models2. Computational portion
• Open "Continuous Growth Models" workbook
• Go to "Data" tab
• Enter observed data
• Go to "Plots—Size" tab to view three diff. models of mold population growth
Linear growth:Constant absolute growth rate (e.g., 20 mm2 / day)
Exponential growth:Constant relative growth rate (e.g., 20% / day)
Logistic growth:Relative growth rate as pop. size (e.g., 0% / day at 700 mm2)
Which model, & what parameter values, can best explain the observed data?
• Go to “Plots—Growth” tab
• These graph the same models & data as before:How do they differ from the previous graphs?
Epidemiological Model
Goal: Introduce students to the process of modeling a biological system
Hook: Predict the outbreak and course of a specific epidemic; model the efficacy of different intervention strategies
Epidemiological Model
1. Building formulas in Excel2. Setting parameters and variables3. Translating biology into math4. Implementing a mathematical model in Excel5. Visualizing & interpreting results
Five-step process:
Epidemiological Model
• Open “SIR Model”
• Simple model: 3 variables, 2 parameters
• From this information, how would you calculate the initial # Susceptible, Infected, Recovered?
• Go to View menu, choose “Formula Bar”
• In Cells B2-D2, enter formulas tocarry out those calculations
Biological Knowledge Mathematical Equations
S I R• How do individuals move from one category to another?
• Write “word equations”; for example:
The # of Susceptibles at
Time 1=
The # of Susceptibles at
Time 0±
The # of newly infected
Susceptibles? ?
• Write formulas for: # newly infected Susceptibles# newly recovered Infecteds
–
Future Directions
• More thorough documentation on biology, math, Excel
• Pre-built curricular resources: “I need something NOW!”
• More modules & improvements to current ones:share resources among community of ESTEEM users